Car Price Prediction from Car Dekho

Table of Contents

  1. Data Preprocessing
  2. Null Value Imputation
  3. EDA
  4. Base Model
  5. Testing Assumptions of Linear Regression
  6. Final Models
In [1]:
# importing required libraries

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
import seaborn as sns 

# for pandas profiling
import pandas_profiling as pp
In [2]:
dataset = pd.read_csv('data/Car details v3.csv')
dataset.head(5)
Out[2]:
name year selling_price km_driven fuel seller_type transmission owner mileage engine max_power torque seats
0 Maruti Swift Dzire VDI 2014 450000 145500 Diesel Individual Manual First Owner 23.4 kmpl 1248 CC 74 bhp 190Nm@ 2000rpm 5.0
1 Skoda Rapid 1.5 TDI Ambition 2014 370000 120000 Diesel Individual Manual Second Owner 21.14 kmpl 1498 CC 103.52 bhp 250Nm@ 1500-2500rpm 5.0
2 Honda City 2017-2020 EXi 2006 158000 140000 Petrol Individual Manual Third Owner 17.7 kmpl 1497 CC 78 bhp 12.7@ 2,700(kgm@ rpm) 5.0
3 Hyundai i20 Sportz Diesel 2010 225000 127000 Diesel Individual Manual First Owner 23.0 kmpl 1396 CC 90 bhp 22.4 kgm at 1750-2750rpm 5.0
4 Maruti Swift VXI BSIII 2007 130000 120000 Petrol Individual Manual First Owner 16.1 kmpl 1298 CC 88.2 bhp 11.5@ 4,500(kgm@ rpm) 5.0
In [3]:
dataset.shape
Out[3]:
(8128, 13)
In [4]:
dataset.info()

<class 'pandas.core.frame.DataFrame'>
RangeIndex: 8128 entries, 0 to 8127
Data columns (total 13 columns):
 #   Column         Non-Null Count  Dtype  
---  ------         --------------  -----  
 0   name           8128 non-null   object 
 1   year           8128 non-null   int64  
 2   selling_price  8128 non-null   int64  
 3   km_driven      8128 non-null   int64  
 4   fuel           8128 non-null   object 
 5   seller_type    8128 non-null   object 
 6   transmission   8128 non-null   object 
 7   owner          8128 non-null   object 
 8   mileage        7907 non-null   object 
 9   engine         7907 non-null   object 
 10  max_power      7913 non-null   object 
 11  torque         7906 non-null   object 
 12  seats          7907 non-null   float64
dtypes: float64(1), int64(3), object(9)
memory usage: 825.6+ KB
In [5]:
dataset.describe()
Out[5]:
year selling_price km_driven seats
count 8128.000000 8.128000e+03 8.128000e+03 7907.000000
mean 2013.804011 6.382718e+05 6.981951e+04 5.416719
std 4.044249 8.062534e+05 5.655055e+04 0.959588
min 1983.000000 2.999900e+04 1.000000e+00 2.000000
25% 2011.000000 2.549990e+05 3.500000e+04 5.000000
50% 2015.000000 4.500000e+05 6.000000e+04 5.000000
75% 2017.000000 6.750000e+05 9.800000e+04 5.000000
max 2020.000000 1.000000e+07 2.360457e+06 14.000000
In [6]:
profile = pp.ProfileReport(dataset)
profile.to_notebook_iframe()

Summarize dataset: 100%|██████████| 26/26 [00:25<00:00,  1.00it/s, Completed]
Generate report structure: 100%|██████████| 1/1 [00:19<00:00, 19.97s/it]
Render HTML: 100%|██████████| 1/1 [00:04<00:00,  4.13s/it]

Data Preprocessing

In [7]:
dataset.isnull().sum()
Out[7]:
name               0
year               0
selling_price      0
km_driven          0
fuel               0
seller_type        0
transmission       0
owner              0
mileage          221
engine           221
max_power        215
torque           222
seats            221
dtype: int64
In [8]:
# Cleaning Mileage column

# filling nulls with zero values
dataset['mileage'] = dataset['mileage'].fillna('0 kmpl')

# splitting numeric data
mileage=[]
for i in dataset['mileage'].str.split(' '):
    mileage.append(float(i[0]))

# storing the numeric data
dataset['mileage'] = mileage

# restoring the nulls in the data
dataset['mileage'] = dataset['mileage'].replace({0:np.nan})

# sanity check 
dataset['mileage']
Out[8]:
0       23.40
1       21.14
2       17.70
3       23.00
4       16.10
        ...  
8123    18.50
8124    16.80
8125    19.30
8126    23.57
8127    23.57
Name: mileage, Length: 8128, dtype: float64
In [9]:
# Cleaning Engine column

# filling nulls with zero values
dataset['engine'] = dataset['engine'].fillna('0 CC')

# splitting numeric data
engine=[]
for i in dataset['engine'].str.split(' '):
    engine.append(int(i[0]))

# storing the numeric data
dataset['engine'] = engine

# restoring the nulls in the data
dataset['engine'] = dataset['engine'].replace({0:np.nan})

# sanity check 
dataset['engine']
Out[9]:
0       1248.0
1       1498.0
2       1497.0
3       1396.0
4       1298.0
         ...  
8123    1197.0
8124    1493.0
8125    1248.0
8126    1396.0
8127    1396.0
Name: engine, Length: 8128, dtype: float64
In [10]:
# Cleaning max_power column

# filling nulls with zero values
dataset['max_power'] = dataset['max_power'].replace({'0':'0 bhp',' bhp':'0 bhp',np.nan:'0 bhp'})

# splitting numeric data
power=[]
for i in dataset['max_power'].str.split(' '):
    power.append(float(i[0]))

# storing the numeric data
dataset['max_power'] = power

# restoring the nulls in the data
dataset['max_power'] = dataset['max_power'].replace({0:np.nan})

# sanity check 
dataset['max_power']
Out[10]:
0        74.00
1       103.52
2        78.00
3        90.00
4        88.20
         ...  
8123     82.85
8124    110.00
8125     73.90
8126     70.00
8127     70.00
Name: max_power, Length: 8128, dtype: float64
In [11]:
# creating a new columns with only car brand and model name
dataset['car'] = [' '.join(i[:2]) for i in dataset['name'].str.split(' ')]

# sanity check
dataset['car']
Out[11]:
0        Maruti Swift
1         Skoda Rapid
2          Honda City
3         Hyundai i20
4        Maruti Swift
            ...      
8123      Hyundai i20
8124    Hyundai Verna
8125     Maruti Swift
8126      Tata Indigo
8127      Tata Indigo
Name: car, Length: 8128, dtype: object
In [12]:
# Dropping torque column 
dataset.drop(columns=['torque'],inplace=True)
dataset.drop(columns=['name'],inplace=True)
In [13]:
dataset.isnull().sum()
Out[13]:
year               0
selling_price      0
km_driven          0
fuel               0
seller_type        0
transmission       0
owner              0
mileage          238
engine           221
max_power        222
seats            221
car                0
dtype: int64

Null Value Imputation

In [14]:
null_cars = dataset.groupby('car').mean()['mileage'].sort_values().tail(11).index
In [15]:
x = pd.DataFrame()
for i in null_cars:
    x=pd.concat([x,dataset[dataset['car']==i]],axis=0)
In [16]:
dataset = dataset.drop(index=[31, 5005, 7538, 1347, 1216, 1432, 1815, 2867, 3922, 5385, 5451,
             316,  535, 1933, 6516, 7275, 7528, 7337, 6730, 3310, 2959, 3456]).reset_index(drop=True)
In [17]:
# directly filling these columns with the respective means in there by the grouping of car
dataset[['year', 'selling_price', 'km_driven', 'mileage', 'engine', 'max_power',
       'seats']]=dataset.groupby("car").transform(lambda x: x.fillna(x.mean()))
In [18]:
# sanity check
dataset.isnull().sum()
Out[18]:
year             0
selling_price    0
km_driven        0
fuel             0
seller_type      0
transmission     0
owner            0
mileage          0
engine           0
max_power        0
seats            0
car              0
dtype: int64

EDA

In [19]:
dataset.dtypes
Out[19]:
year               int64
selling_price      int64
km_driven          int64
fuel              object
seller_type       object
transmission      object
owner             object
mileage          float64
engine           float64
max_power        float64
seats            float64
car               object
dtype: object
In [20]:
# Converting seats to categorical column
dataset['seats'] = dataset['seats'].astype('O')
In [21]:
# Creating a new column Age from Year
dataset['Age'] = 2021 - dataset['year']
In [22]:
# dropping years col
dataset.drop(columns=['year'],inplace=True)
In [23]:
# Separating numerical and categorical columns
df_int = dataset.select_dtypes(include=np.number)
df_cat = dataset.select_dtypes(include='O')
In [24]:
# Correlation matrix
sns.heatmap(df_int.corr(),annot=True,cmap=plt.cm.Blues_r)
plt.show()

Age and Selling price is neagtively coreleated

selling_price and max_power is strongly positive coreleated

max_power and engine is positivley corelated

age and km _driven are positve corelated

In [25]:
for i in df_int.columns:
    plt.boxplot(df_int[i])
    plt.xlabel(i)
    plt.show()
In [26]:
df_int.describe().loc['mean']
Out[26]:
selling_price    638887.892055
km_driven         69839.254133
mileage              19.450891
engine             1454.372268
max_power            91.076373
Age                   7.167407
Name: mean, dtype: float64
In [27]:
sns.scatterplot(data = dataset,x = 'selling_price',y= 'mileage',hue = 'fuel')  # 
plt.grid()
plt.show()

CNG cars are most fuel efficient and cost effective.

Mileage for petrol and diesel car is within the range of 10-30 Kmpl

In [28]:
plt.figure(figsize=(15,8))
sns.stripplot(y=dataset['selling_price'],x=dataset['fuel'])
plt.grid()
plt.show()

Petrol cars are comparitively cheaaper in comparison to Diesel cars(under Rs. 2 lakhs)

High Concentration of Petrol Cars in the selling price range : 0-2 lakhs

High Concentration of Diesel Cars in the selling price range : 0-6 lakhs

In [29]:
plt.figure(figsize=(15,8))
sns.stripplot(y=dataset['selling_price'],x=dataset['owner'])
plt.grid()
plt.show()

It is clearly visible that selling price is decreasing as the pre owner no increases.

In [30]:
plt.figure(figsize=(12,8))
df_int.groupby(['Age']).mean()['selling_price'].plot(kind='line',grid=True,label='Selling_price')
df_int.groupby(['Age']).mean()['km_driven'].plot(kind='line',grid=True)
plt.legend()
plt.show()

As age increases selling price decreases and Kms driven increases

In [31]:
from warnings import filterwarnings
filterwarnings('ignore')
for i in df_cat.iloc[:,:-1]:
    plt.figure(figsize=(10,7))
    sns.countplot(df_cat[i])
    plt.show()

Diesel cars are more in our dataset as compared to other fuel types.

Individual seller type is in majority in seller type.

Maximum cars in our dataset is haivng seating capacity of 5.

Manual cars are more as compared to automatic cars

In [32]:
sns.countplot(data = dataset,x='fuel')
plt.show()
In [33]:
dataset['seats']=dataset['seats'].map(lambda x: round(x))
In [34]:
pd.crosstab(dataset['fuel'],dataset['seller_type']).plot(kind='bar',figsize=(12,8))
plt.show()

No Trustmark ,dealer seller types in LPG and CNG fuel type.

In [35]:
pd.crosstab(dataset['fuel'],dataset['transmission']).plot(kind='bar',figsize=(12,8))
plt.show()

No automatic tranmission in LPG and CNG duel type

Manual transmission is predominant in both Diesel and Petrol cars

In [36]:
pd.crosstab(dataset['fuel'],dataset['owner']).plot(kind='bar',figsize=(12,8))
plt.show()

Test drive cars are available only in petrol fuel type

First Owner cars is predominant in both Diesel and Petrol fuel type

Base Model

Label Encoding the categorical variables

In [37]:
from sklearn.preprocessing import LabelEncoder
le = LabelEncoder()
label_cat = pd.DataFrame()

for i in df_cat.columns:
    label_cat[i] = le.fit_transform(df_cat[i])
In [38]:
X_base = pd.concat([label_cat,df_int],axis=1)
X_base
Out[38]:
fuel seller_type transmission owner seats car selling_price km_driven mileage engine max_power Age
0 1 1 1 0 3 120 450000 145500 23.40 1248.0 74.00 7
1 1 1 1 2 3 154 370000 120000 21.14 1498.0 103.52 7
2 3 1 1 4 3 55 158000 140000 17.70 1497.0 78.00 15
3 1 1 1 0 3 75 225000 127000 23.00 1396.0 90.00 11
4 3 1 1 0 3 120 130000 120000 16.10 1298.0 88.20 14
... ... ... ... ... ... ... ... ... ... ... ... ...
8101 3 1 1 0 3 75 320000 110000 18.50 1197.0 82.85 8
8102 1 1 1 1 3 72 135000 119000 16.80 1493.0 110.00 14
8103 1 1 1 0 3 120 382000 120000 19.30 1248.0 73.90 12
8104 1 1 1 0 3 162 290000 25000 23.57 1396.0 70.00 8
8105 1 1 1 0 3 162 290000 25000 23.57 1396.0 70.00 8

8106 rows × 12 columns

In [39]:
y = X_base['selling_price'].values
In [40]:
X_base.drop(columns=['selling_price'],inplace=True)

train test split

In [41]:
from sklearn.model_selection import train_test_split
X_train,X_test, y_train, y_test = train_test_split(X_base,y,random_state=8)

Linear Regression

In [42]:
from sklearn.linear_model import LinearRegression
lr = LinearRegression()
In [43]:
lr.fit(X_train,y_train)
Out[43]:
LinearRegression()
In [44]:
lr.score(X_train,y_train)
Out[44]:
0.6823443600613711
In [45]:
lr.score(X_test, y_test)
Out[45]:
0.6644841275556826
In [46]:
import statsmodels.api as sm
model = sm.OLS(y_train,sm.add_constant(X_train)).fit()
print(model.summary())

                            OLS Regression Results                            
==============================================================================
Dep. Variable:                      y   R-squared:                       0.682
Model:                            OLS   Adj. R-squared:                  0.682
Method:                 Least Squares   F-statistic:                     1185.
Date:                Mon, 19 Apr 2021   Prob (F-statistic):               0.00
Time:                        18:20:56   Log-Likelihood:                -87855.
No. Observations:                6079   AIC:                         1.757e+05
Df Residuals:                    6067   BIC:                         1.758e+05
Df Model:                          11                                         
Covariance Type:            nonrobust                                         
================================================================================
                   coef    std err          t      P>|t|      [0.025      0.975]
--------------------------------------------------------------------------------
const         1.399e+05   1.01e+05      1.389      0.165   -5.76e+04    3.37e+05
fuel         -1.462e+04   8365.835     -1.748      0.081    -3.1e+04    1778.192
seller_type  -2.241e+05   1.59e+04    -14.123      0.000   -2.55e+05   -1.93e+05
transmission -5.126e+05   2.22e+04    -23.040      0.000   -5.56e+05   -4.69e+05
owner        -8845.3406   5543.661     -1.596      0.111   -1.97e+04    2022.203
seats        -1.169e+04   4772.144     -2.450      0.014    -2.1e+04   -2338.931
car           -525.4509    133.073     -3.949      0.000    -786.322    -264.580
km_driven       -0.9223      0.118     -7.825      0.000      -1.153      -0.691
mileage       1.474e+04   2563.788      5.749      0.000    9712.301    1.98e+04
engine         102.6450     27.101      3.787      0.000      49.517     155.773
max_power     1.246e+04    309.117     40.323      0.000    1.19e+04    1.31e+04
Age          -3.181e+04   2073.759    -15.339      0.000   -3.59e+04   -2.77e+04
==============================================================================
Omnibus:                     3172.933   Durbin-Watson:                   1.982
Prob(Omnibus):                  0.000   Jarque-Bera (JB):            49938.916
Skew:                           2.128   Prob(JB):                         0.00
Kurtosis:                      16.381   Cond. No.                     1.57e+06
==============================================================================

Warnings:
[1] Standard Errors assume that the covariance matrix of the errors is correctly specified.
[2] The condition number is large, 1.57e+06. This might indicate that there are
strong multicollinearity or other numerical problems.
In [47]:
residual = model.resid

Testing Assumptions of Linear Regression

Test for Normality

In [48]:
# Ho: Predictor variable is Normal
# H1: Predictor variable is not Normal

from scipy.stats import jarque_bera
jarque_bera(residual)
Out[48]:
Jarque_beraResult(statistic=49938.91561736401, pvalue=0.0)

As our p-value is less than 0.05, we reject our null hypothesis that our data is normal

Test for Linearity/ Homoscedasticity/ Autocorrelation

In [49]:
fitted = model.fittedvalues

sns.scatterplot(fitted,residual)
plt.show()

As we can see that our data is non-linear, hence we can say that the data is non linear

As the residuals are highly varying, they are Heteroscedastic

As we observe no pattern in the residuals, we can say that there is no autocorrealation present in the data

Test for Multicollinearity

In [50]:
from statsmodels.stats.outliers_influence import variance_inflation_factor

vif_data = pd.DataFrame()
vif_data["feature"] = X_base.columns

vif_data["VIF"] = [variance_inflation_factor(X_base.values, i)
                          for i in range(len(X_base.columns))]
  
print(vif_data)

         feature        VIF
0           fuel   5.000426
1    seller_type   6.831443
2   transmission  11.510250
3          owner   1.901692
4          seats  10.128328
5            car   6.473541
6      km_driven   3.623124
7        mileage  15.951442
8         engine  40.280221
9      max_power  22.759468
10           Age   6.744922

Final Models

In [51]:
# Decision Tree Regressor
from sklearn.tree import DecisionTreeRegressor
dtr = DecisionTreeRegressor()
dtr.fit(X_train,y_train)
Out[51]:
DecisionTreeRegressor()
In [52]:
dtr.score(X_train,y_train)
Out[52]:
0.9996683658883604
In [53]:
dtr.score(X_test,y_test)
Out[53]:
0.9458535008071733
In [54]:
# Random Forest Regressor
from sklearn.ensemble import RandomForestRegressor
rfr = RandomForestRegressor()
rfr.fit(X_train,y_train)
Out[54]:
RandomForestRegressor()
In [55]:
rfr.score(X_train,y_train)
Out[55]:
0.9956138951824747
In [56]:
rfr.score(X_test,y_test)
Out[56]:
0.9558544808283851
In [57]:
# installing xgboost
!pip3 install xgboost

Requirement already satisfied: xgboost in f:\anaconda3\lib\site-packages (1.3.3)
Requirement already satisfied: scipy in f:\anaconda3\lib\site-packages (from xgboost) (1.5.0)
Requirement already satisfied: numpy in f:\anaconda3\lib\site-packages (from xgboost) (1.18.5)
In [58]:
# XGBoost Regressor
import xgboost as xgb
xgb_reg = xgb.XGBRegressor(objective ='reg:squarederror', 
                          colsample_bytree = 0.3, 
                          learning_rate = 0.1, 
                          max_depth = 10, 
                          alpha = 1, 
                          n_estimators = 250)
xgb_reg.fit(X_train,y_train)
Out[58]:
XGBRegressor(alpha=1, base_score=0.5, booster='gbtree', colsample_bylevel=1,
             colsample_bynode=1, colsample_bytree=0.3, gamma=0, gpu_id=-1,
             importance_type='gain', interaction_constraints='',
             learning_rate=0.1, max_delta_step=0, max_depth=10,
             min_child_weight=1, missing=nan, monotone_constraints='()',
             n_estimators=250, n_jobs=12, num_parallel_tree=1, random_state=0,
             reg_alpha=1, reg_lambda=1, scale_pos_weight=1, subsample=1,
             tree_method='exact', validate_parameters=1, verbosity=None)
In [59]:
xgb_reg.score(X_train,y_train)
Out[59]:
0.9974518821156302
In [60]:
xgb_reg.score(X_test,y_test)
Out[60]:
0.9476996667548025

Therefore the best model for this data is Random Forest Regressor